Matrices ─ Algebra, Analysis and Applications

This volume deals with advanced topics in matrix theory using the notions and tools from algebra, analysis, geometry, and numerical analysis. It consists of seven chapters that are loosely connected. The very personal choice of topics reflects the subjects that the author was actively working on in the last 40 years. Many results appear for the first time in the volume. Readers will encounter various properties of matrices with entries in integral domains, canonical forms for similarity, and notions of analytic, pointwise and rational similarity of matrices with entries which are locally analytic functions in one variable. This volume also discusses various properties of operators in inner product space, with tensor products and other concepts in multilinear algebra, and the theory of nonnegative matrices. It will be of great use to graduate students and researchers working in pure and applied mathematics, bioinformatics, computer science, engineering, operation research, physics and statistics.